Abstract
Confused terms appear to signify more than one entity. Carnap (Meaning and necessity, University of Chicago Press, Chicago, 1956) maintained that any putative name that is associated with more than one object in a relevant universe of discourse fails to be a genuine name. Although many philosophers have agreed with Carnap, they have not always agreed among themselves about the truth-values of atomic sentences containing such terms. Some hold that such atomic sentences are always false, and others claim they are always truth-valueless. Field (J Philos 70:462–481, 1973) maintained that confused terms can still refer, albeit partially, and offered a supervaluational account of their semantic properties on which some atomic sentences with confused terms can be true. After outlining many of the most important theoretical considerations for and against various semantic theories for such terms, we report the results of a study designed to investigate which of these accounts best accords with the truth-value judgments of ordinary language users about sentences containing these terms. We found that naïve participants view confused names as capable of successfully referring to one or more objects. Thus, semantic theories that judge them to involve total reference failure do not comport well with patterns of ordinary usage.
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Notes
Thanks to an anonymous reviewer for helping us make this formulation more precise.
The phrase ‘free logic’ abbreviates ‘logic free of any existential presuppositions.’ In other words, free logics do not assume that every individual constant, i.e. grammatical name, refers to something that exists in the domain of quantification. For overviews of free logic, see Nolt (2010) and Lambert (2001).
As a reviewer pointed out to us, the phrase ‘referring to too many things’ should not be taken completely literally here. One could reasonably hold that any purported name that is applied to multiple individuals fails to refer entirely, i.e. refers to nothing, on the grounds that all real, genuine reference must uniquely identify an individual. We explore this position below, so we do not want to define it out of existence here.
We use ‘truth-valueless’ to abbreviate ‘neither true nor false.’ This is a slight abuse of terminology, because if there are further truth values in addition to the standard two True and False, then a sentence which has one of those other truth-values is neither true nor false, but is not truth-valueless. This abuse of terminology is harmless for present purposes, since we did not ask subjects about exotic truth-values in our study.
Thanks to an anonymous reviewer at JoLLI for correcting a mistake we made regarding these issues in an earlier draft.
For arguments in favor of accepting this apparently counterintuitive consequence, see Burge (Burge 1974, IV).
The naïve version of supervaluational semantics for multiply-signifying names, found in Field (1973), has this problem. However, this problem can be avoided if one uses a more sophisticated supervaluational semantics, which will be briefly described later in this paragraph.
An argument is backwards-falsehood preserving iff, whenever the conclusion is false, at least one of the premises is also false.
This is achieved by adding a special rule for atomic formulas containing identity. Specifically, where a and b can be names or variables, if a formula of the form ‘a = b’ contains exactly one multiply-signifying name, then ‘a = b’ is false.
Actually, the next proposal (3c) declares more sentences true; however, it does so by declaring many sentences both true and false, a conclusion non-dialethists will find unwelcome.
Note that this is a further dimension along which the contextualist position is underspecified: in cases where reference is genuinely indeterminate by the contextualist’s lights, does the contextualist adopt a neutral, negative, or positive semantics?
Additionally, as we will see in Table 2, our survey participants tended to respond that Fred can utter truths about Ant A using the name ‘Charley’ while looking at Ant A.
Lewis describes this position as providing an “intuitive interpretation” of the logics RM and LP. Priest specifically describes his proposal as a proper sub-logic of LP (1995, 365), which is unsurprising, given that he developed LP and defends it on grounds independent of confused terms.
McLeish (2006, 188, 189), the proponent of this semantics, explicitly bites both of these bullets.
For modus ponens (p → q, p, ∴ q): let p be false on some disambiguations but true on others (and thus true on McLeish’s semantics, and both true and false on Lewis-Priest’s semantics), and let q be false on all disambiguations (and thus false on both McLeish’s and Lewis-Priest’s semantics). On this assignment, p → q will be evaluated true by McLeish, and both true and false by Lewis-Priest, since there must be at least one disambiguation where p is false. The counterexample for modus tollens is similar.
One might initially think that the neutral semantics cannot say (b) ‘Both large ants,’ on the grounds that if we have Ant A and Ant B on the left-hand side of the identity-proposition, and Ant A and Ant B on the right-hand side as well, then ‘Charley = Charley’ would have to be true, contra the neutral semantics. But merely having the same stuff in the two slots of an identity-proposition does not guarantee a true proposition; compare, in standard first-order textbook logic with identity, the schemas ‘P = P’ and ‘p = p’, where P is any predicate and p is any sentence. These schemas never have true instances, because they are ungrammatical; the neutral-semantics proponent could consider the sentence ‘Charley = Charley’ ungrammatical, on the grounds that ‘Charley’ is not a name, or she could consider the sentence to violate semantic rules instead. (This reasoning holds mutatis mutandis for negative semantics, too; see the next paragraph).
Participants might sometimes select ‘True’ to indicate the thought that it could be true on some occasions that ‘Charley’ refers to Ant A. Participants could also select ‘False,’ since it would be false on different occasions. These answers would of course depart from the literal meaning of the answer choices ‘True’ and ‘False,’ since on the hypothesized interpretation participants would instead be expressing the idea that (5) ‘Could be true’ or ‘Could be false.’ But the puzzling nature of the task could lead some participants to answer in this fashion. For similar reasons, participants might also select ‘Both true and false,’ since things could go either way, depending on how the context ended up being specified. Or they could say ‘Neither true nor false’ or ‘Don’t know/can’t tell,’ on the grounds that not enough context was provided to determine a truth-value.
Q2: χ2(4, N = 166) = 324.96, p < .00001. Q3: χ2(4, N = 165) = 406.12, p < .00001. Q4: χ2(4, N = 167) = 397.10, p < .00001. Q5: χ2(4, N = 167) = 38.06, p < .00001. Q6: χ2(4, N = 165) = 47.33, p < .00001. Q7: χ2(4, N = 167) = 468.60, p < .00001. Q8: χ2(4, N = 164) = 327.71, p < .00001. Q9: χ2(4, N = 164) = 192.46, p < .00001. Q10: χ2(2, N = 164) = 72.89, p < .00001. Q11a: χ2(4, N = 86) = 24.12, p < .0001. Q11b: χ2(4, N = 77) = 30.34, p < .00001.
χ2(8, N = 16,533) = 3766.03, p < .000000001, Cramér’s V = .48. N was obtained in the following fashion: 167 participants who answered the comprehension question correctly x 11 questions answered by each participant x 9 accuracy scores. Accuracy scores for both versions of supervaluationalism were considered and two different accuracy scores for contextualism were entered into the analysis.
χ2(1, N = 3674) = 67.26, p < .000000001 (uncorrected), Cramér’s V = .14.
χ2(1, N = 3674) = 1.43, p = .23 (uncorrected).
χ2(1, N = 3674) = 84.33, p < .000000001 (uncorrected), Cramér’s V = .15.
We thank an anonymous JoLLI referee for preventing us from drawing a stronger conclusion from this data than was warranted.
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Acknowledgements
The authors would like to thank helpful audiences at the 2018 Society for Exact Philosophy, the UK XPhi Conference 2018, and very insightful and careful referees for the Journal of Logic, Language, and Information. One reviewer in particular helped make this paper much better than it previously was.
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Frost-Arnold, G., Beebe, J.R. Confused Terms in Ordinary Language. J of Log Lang and Inf 29, 197–219 (2020). https://doi.org/10.1007/s10849-019-09300-8
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DOI: https://doi.org/10.1007/s10849-019-09300-8